The product of two complex numbers x and y is defined to be z=xRyR−x1y1+i(xRy1+x1yR), where x=xR+ix1, y=yR+iy1 and i is an imaginary number, or the square root of negative one, with i2=−1. This complex multiplication of x and y is calculated in a variety of contexts, and it has been recognized that it will be highly advantageous to perform this calculation faster and more efficiently.